Ariana starts with 100 milligrams of a radioactive substance. The amount of the substance decreases by 20% each week for a number of weeks, w. The expression 100(1 – 0.2)^w finds the amount of radioactive substance remaining after w weeks. Which statement about this expression is true?
It is the difference between the initial amount and the percent decrease.
It is the initial amount raised to the decay factor after w weeks.
It is the difference between the initial amount and the decay factor after w weeks.
It is the product of the initial amount and the decay factor after w weeks.
The correct statement is: It is the product of the initial amount and the decay factor after w weeks.
Explanation: The expression (100(1 – 0.2)^w) represents the initial amount (100 milligrams) multiplied by the decay factor ((1 – 0.2)) raised to the power of (w) (the number of weeks). Here, ((1 – 0.2)) represents the remaining percentage of the substance after each week, which is 80% (or 0.8). Thus, it models the diminishing amount of the substance over time as it decreases by 20% each week.